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Definition:

The multiples of a number are all the numbers that are the result of the product of that number with any other integer. For example: the first 10 multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 and are obtained by multiplying 3 with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 respectively.

Practice questions:

Q1: List the first 10 multiples of 5

A1: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Q2: Match the following

 Multiples of 5 10, 12, 14, 16, 18 Multiples of 7 5, 10, 15, 20, 25 Multiples of 10 25, 50, 75, 100 Multiples of 25 14, 21, 28, 35, 42 Multiples of 2 50, 60, 70, 80, 90

A2: 1 - b, 2 - d, 3 - e, 4 - c, 5 - a

Common Multiples

Consider the multiples of 5 and 10

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70….

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100….

If you notice there are some numbers that are multiples of 5 and 10 such as 10, 20, 30, 40, 50, 60, 70 etc. Such numbers that are multiples of two or more numbers are referred to as common multiples of those numbers.

Common multiples can also be represented by Venn diagrams .

Lowest Common Multiple (LCM)

In the above example, the number 10 is the lowest common multiple to appear in both lists and is called the Least Common multiple of 5 and 10.

The Least Common Multiple of two or more numbers is defined as the smallest possible number that is a multiple of those two or more numbers.

Practice questions:

Q1: List the first three common multiples of 2 and 5.

A1: Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55

The first three common multiples of 2 and 5 are 10, 20, 30.

Q2: Find the Least common multiple of 3 and 7.

A2: The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33…

Multiples of 7 are 7, 14, 21, 28…

The LCM of 3 and 7 is 21.

Q3: Find the Least common multiple of 3, 5 and 15.

A3: The multiples of 3 are 3, 6, 9, 12, 15, 18, 21…

Multiples of 5 are 5, 10, 15, 20…

Multiples of 15 are 15, 30…

The least common multiple of 3, 5 and 15 is 15.  Important facts about multiples:

• Every number is a multiple of itself.

For example: the multiples of 3 are 3x1=3, 3x2=6, 3x3=9 and so on.

• Every multiple of a number is greater than or is equal to that number.

For example: the multiples of 8 are 8, 16, 24, 32, 40 and so on. All are greater than or equal to the number 8.

• The number of multiples of a given number are infinite.

For example: the multiples of 4 are 4,8,12,16, 20, 24, 28, 32, 36, 40, 44, 48 and the list goes on.

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